Probing late-time deviations from $\Lambda$CDM with a quadratic dark energy expansion

We investigate the observational viability of a quadratic dark energy expansion (QDEE) model as a phenomenological extension of the standard $\Lambda\mathrm{CDM}$ cosmological framework. This approach introduces the additional degrees of freedom that permit mild late-time deviations from a constant dark-energy component while preserving the standard early-Universe behavior. We constrain the model using a comprehensive combination of cosmological datasets, including Planck 2018 cosmic microwave background (CMB) measurements, Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) and South Pole Telescope (SPT-3G) data, Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2), and the Pantheon Plus type Ia supernova compilation. Our results show that the QDEE framework shifts the inferred Hubble constant toward higher values relative to $\Lambda\mathrm{CDM}$, partially alleviating the tension with local measurements while remaining consistent with early-Universe constraints. Bayesian model comparison indicates strong evidence in favor of this framework over standard $\Lambda\mathrm{CDM}$ across multiple dataset combinations. Posterior predictive checks further demonstrate that the model yields predictions consistent with the observed data within statistical uncertainties.